Let G be a group acting on a tree X such that all edge stabilizers are finite. We extend Bestvina-Handel’s theory of train tracks for automorphisms of free groups to automorphisms of G which permute vertex stabilizers. Using this extension we show that there is an upper bound depending only on G for the complexity of the graph of groups decomposition of the fixed subgroups of such automorphisms...

For any field k we fix an algebraic closure of k, denoted by k. For a variety X ⊂ P k we set X = X×k k, we say thatX is smooth ifX is regular, and we let AutX denote the group of k-automorphisms ofX, while LinX denotes the group of linear automorphisms of X , i.e., automorphisms induced by a linear transformation of the coordinates of P. The following theorem was proved by Poonen, see [Po2], Th...

In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.

The inner automorphisms of a group G can be characterized within the category of groups without reference to group elements: they are precisely those automorphisms of G that can be extended, in a functorial manner, to all groups H given with homomorphisms G→ H. (Precise statement in §1.) The group of such extended systems of automorphisms, unlike the group of inner automorphisms of G itself, is...

First we show that any group of automorphisms of null-entropy of a projective hyperkähler manifold M is almost abelian of rank at most ρ(M) − 2. We then characterize automorphisms of a K3 surface with nullentropy and those with positive entropy in algebro-geometric terms. We also give an example of a group of automorphisms which is not almost abelian in each dimension.

We determine which simple algebraic groups of type D4 over arbitrary fields of characteristic different from 2 admit outer automorphisms of order 3, and classify these automorphisms up to conjugation. The criterion is formulated in terms of a representation of the group by automorphisms of a trialitarian algebra: outer automorphisms of order 3 exist if and only if the algebra is the endomorphis...

The trialitarian automorphisms considered in this paper are the outer automorphisms of order 3 of adjoint classical groups of type D4 over arbitrary fields. A one-to-one correspondence is established between their conjugacy classes and similarity classes of symmetric compositions on 8-dimensional quadratic spaces. Using the known classification of symmetric compositions, we distinguish two conj...

We study the group of all "R-automorphisms" of a countable equivalence relation R on a standard Borel space, special Borel automorphisms whose graphs lie in R. We show that such a group always contains periodic maps of each order sufficient to generate R . A construction based on these periodic maps leads to totally nonperiodic R-automorphisms all of whose powers have disjoint graphs. The prese...

§0. Introduction In 1912 Max Dehn formulated fundamental problems concerning a group given by generators and relations. One of these, the conjugacy problem, asks whether there is an algorithm to decide whether two words in the generators represent conjugate elements of the group. Dehn himself gave an elegant solution to this problem in the case when the group is the fundamental group of a close...